MUSICAL TIME The word "rhythm" is derived from a Greek word meaning "measure, measured motion." In a general sense, rhythm is the organization of events into patterns which are "measurable." In music, rhythm is the organization of time into patterns of relative loudness versus relative quite. Just as space is made perceivable and measurable by objects differ- entiating one location from another, so time is perceived by relationships of events: the heart contracting and expanding; the sun appearing overhead or setting; the sound of a drop of water falling, then another...and another... Of course, all these events are spatial as well as temporal, and in our associating the two we comprehend the elementary continuum which they form. In less formal language, rhythm is the "swing" of things, the flow of events as they relate one to another. Rhythm is felt to be generative. It propels events, gives life to them, stimulates our sense that the elements of life create patterns. Rhythm occurs at all levels of our experience: the cycles of our lives, our heart's pulse, the hours, days, weeks, and months into which we make the divisions of our time; changing seasons; design of flowers, magne- tic fields, snowflakes, galaxies... This may be why the rhythmic patterns of sound in music have such a fundamental effect upon us. Musical rhythm is the articulation of time, which resonates with all the other rhythms we instinctively understand. Rhythm, pulse, cycles of the seasons, the days, our blood, life and death, questions of why and how and what shaped into communal expressions danced and sung and pounded out on drums; rhythms and sounds and silences and gestures groping for ...meaning... PRELIMINARY EXERICISE The relatively longer versus shorter sounds of words have been traditionally represented by = long and = short. <1> = Enter text. At prompt, write a text no longer than one line with a maximum of 20 syllables. <2> = Enter number of syllables in text. <3> = Enter "S" for Short, "L" for long, trying to produce an approximation of the rhythm of your text.

= Play rhythm. [You may continue above sequence as many times as you like.] PULSE In music, time is measured by rhythm, an articulation of time created by contrasts in relative loudness or intensity levels. These contrasts cause pulses to occur, which may be either regular (periodic) or irregular (nonperiodic). Pulse is distinguished by difference between emphasis (oomph!) and de-emphasis (pah) or any combination of these contrasting events: We know that this computer is not capable of varying loudnesses, so the sense of emphasis and de-emphasis just heard was created by varying pitch level. This reinforces the notion that we perceive rhythmic patterns through differences. We are most familiar in traditional music with regular pulse, the articulation of time into periodic recurrence of stress versus nonstress. But rhythm may also be nonperiodic--stress and nonstress occuring irregularly--and much of the beautiful complex- ity of primal music, as well as the exciting tensions of twentieth- century Western music, is created by diverging from regularity of pulse. Pulse is just what we understand it to be in relation to our heart beat: contraction and expansion (called systole and diastole). Pulse is a basic aspect of music which occurs on several levels: a piece of music as a whole is a kind of pulse in relation to the relative silence which surrounds it; there is usually sectional division of structure within the music which creates large-scale pulses of contrasting intensity; and there is a basic pulsation of sound which we commonly refer to as the beat, which is the ongoing, second-to-second, propelling rhythmic force of music, providing the basic sense of motion through time essential to Western music. The beat is what we clap our hands or stamp our feet to, and it is this level of rhythm for which we need to formulate principles of notation in order to read and compose music. PERIODIC RHYTHM 1. Beat Groupings As has been stated, rhythm in music requires the alternation of sound and silence, or relative change in loudness levels. A metronome produces such an alternation. [any key to stop] You have just heard a regular and constantly intense pulse juxta- posed with silence. These pulses are undifferentiated. But if we listen for any length of time, chances are that we begin to hear them in groups, most likely in 2's or 3's. Listen again to a series of beats and hear how easy it is to change from hearing them in groups of 2 to groups of three. [any key to stop] It is possible to hear these beats in larger groupings, of course, but one must consciously add the beats up to 4 or 5 or 6. These larger groupings are more likely heard as combinations of 2 or 3. Undifferentiated beats are essentially as meaningless to us as eternal silence or featureless space. Things seem to come alive only when we perceive change. So it is with rhythm. Just as the ear imposes patterns on consistantly intense beats, so when music is composed, beats are traditionally organized into patterns by emphasising certain beats and underplaying others. And just as the ear most readily organizes undifferentiated beats into groups of 2 and 3, so does composed music most readily deploy these beat patterns. Longer groupings are possible, but just as with the imagined groupings, them are most often heard as combinations of 2- and/or 3-beat groupings. A beat grouping, in the terminology of music, is called a measure. In traditional notation, the measure symbol is a vertical line--the measure or bar line. A 2-beat measure is duple, a 3-beat measure triple, and so on. In the heirarchy of rhythmic levels, the measure is the next duration- al level up from the beat (the next longest). In other words, if the first beat of a measure is listened to as such, it can be heard as establishing a new pulse at a longer duration than the beat: If, on every 4th measure, say, the elements of a piece of music were to combine to emphasize the first beat of that measure above any other beat, yet another level would be established--a pulse every 4 measures: This latter grouping of four measures could be called a musical phrase. How phrases are grouped determines the larger musical structure. The sense of the different levels on which rhythm is operating is important for understanding how patters of rhythms may be built up to shape an entire piece of music, contributing to a sense of forward motion, fullfilling a listener's expectations or thwarting them. EXERCISE 1 1. "H"= (H)ear tune which has periodic rhythm. You may listen to tune as many times as you wish, using "H". 2. "R"= ready to enter the number of beats you perceive per grouping (measure). You get only 1 chance here, since your options are so limited! 3. At the next prompt, enter the number measures in a phrase. 4. "N"=(N)ext tune - up to 10. 5. "P"=(P)rior tune Beat Divisions Careful listening to the tunes in the above exercise will have re- vealed a couple additional pieces of information. One is that most phrases in common tunes are either 2 or 4 measures long. Another is that what is perceived to be the main beat is sometimes divided into shorter sub-pulses. In fact, the sub-pulse may occasionally be confused with the beat, depending upon the tempo (beat rate). In slow tempos, the sub-pulse may assume the role of the beat, in the same way that at very fast tempos, the first beat of each meas- ure may be heard as the beat. Just as a measure may have, at its simplest ordering, either 2 or 3 beats, so a beat may be divided most simply into either 2 or 3 sub-pulses. If the beat is divided into 2 equal sub-pulses, the division is simple; if into 3 equal sub-pulses, the division is compound. By varying combinations of divisions of the beat, beats, measure lengths, and phrase lengths, a great variety of rhythms is possible. In most traditional music of the Western European heritage, the phrase length, measure length, and beat length remain fairly con- stant, but even with the permutations possible at the sub-pulse level, tremendous rhythmic interest can be generated. EXERCISE 2 1. "H"= (H)ear tune which has periodic rhythm. You may listen to tune as many times as you wish, using "H". 2. "R"= ready to enter the perceived divisional value of the beat: SIMPLE, or COMPOUND> 3. "N"=(N)ext tune - up to 10. 4. "P"=(P)rior tune. Non-Periodic Rhythm Beats, measures, and beat divisions, as just discussed, are categories of periodic rhythm, all relating to a steady rate of pulsation. Non-periodic rhythm has no steady underlying pulse rate and therefore does not require symbols for measures, beats, and beat division. Or if these symbols are used, some factor must be added which allows for a changing rate. If a composition is con- ceived in which great flexibility of pulse is desired, it is easier to accomodate this with newly designed symbols and instructions. For instance, an accellerating series of articulations might be represented by a "time" line, read from left to right, with dots standing for the articulations. Thus: . . . . . . . . . . . . ........ visually suggests a slow rate gradually getting faster. The inter- pretation of this could not be precise, and it is this very issue which underlies non-periodicity. To precisely control non-periodi- city requires extraordinary notational as well as performing skill and the results, for the most part, are no better than approximat- ing the same effect with a less precise system. Hit to hear interpretation of the above notation. Levels of Rhythmic Activity The beat is the most basic level rhythmic activity. It is at this level that we tap our foot, snap our fingers...dance. Measures (beat groupings) are a "higher" or "macro" level of rhythmic organization, and beat divisions are "lower" or "micro" level. Our perception of the level of rhythmic activity is entirely dependent upon our perception of tempo (the rate of the beat, measure in beats per minute). This tune is in 3 beats per measure with simple division. Each note heard is a beat length. At this slow tempo, we are likely to start hearing the divisional value (half the beat length) as the beat. At tempos slower than around 50 bpm, we would not tap our feet to the designated beat, but to the division of the beat. The measure at this tempo is clearly heard. At rates anywhere from about 60 to 140 bpm, we have no difficulty responding by matching toe-tapping to the beat. Now the tempo is fast enough that we hear each beat as a division, and we group these into "the beat". Since there were 3 per measure, we now hear 3 units per beat and thus have compound division. Note that you may now hear 2 of these units per measure. THAT MOMENT IS ALWAYS CHANGING...AND WHILE WE ARE THINKING I AM TALKING AND CONTEMPORARY MUSIC IS CHANGING. LIKE LIFE IT CHANGES. IF IT WERE NOT CHANGING IT WOULD BE DEAD, AND, OF COURSE, FOR SOME OF US, SOMETIMES IT IS DEAD, BUT AT ANY MOMENT IT CHANGES AND IS LIVING AGAIN. TALKING FOR A MOMENT ABOUT CONTEMPORARY MILK: AT ROOM TEMPERATURE IT IS CHANGING, GOES SOUR ETC., AND THEN A NEW BOTTLE ETC., UNLESS BY SEPARATING IT FROM ITS CHANGING BY POWDERING IT OR REFRIGERATION (WHICH IS A WAY OF SLOWING DOWN ITS LIVELINESS) (THAT IS TO SAY MUSEUMS AND ACADEMIES ARE WAYS OF PRESERVING) WE TEMPORARILY SEPARATE THINGS FROM LIFE (FROM CHANGING) BUT AT ANY MOMENT DESTRUCTION MAY COME SUDDENLY AND THEN WHAT HAPPENS IS FRESHER (John Cage) RHYTHMIC NOTATION Brief Review - Periodic rhythm is organized into measures of 2, 3, or more beats. Beats are divided into 2 or 3 sub-pulses. If a beat is divided into 2 equal parts, the division is simple. If the beat is divided into 3 equal parts, the division is compound. Labelling Measures Combinations of particular numbers of beats in a measure and how each beat is divided determines how measures are labelled. A 2- beat measure is called duple; 3-beat measure = triple; 4-beat meas- ure = quadruple; 5-beat measure = quintuple, etc. REMEMBER: If the basic beat is divided into 2, the beat is simple; likewise the measure having simple division of the beat. If the basic beat is divided into 3, the beat is compound; likewise the measure having compound division of the beat. Thus, a measure containing 2 beats (duple), which are divided into 2 sub-pulses (simple) is labelled duple simple. Duple and quadruple measures, either simple or compound, are often difficult to distin- guish with the phrase structure of the piece providing the only basis upon which to make the distinction. A measure containing a given number of beats (2,3,4, etc), each of which is divided into 3 sub-pulses would be a duple, triple, quad- ruple, etc., compound measure. Compound meter will be discussed at greater length later. SIMPLE DIVISION Notation of the Beat Its Division and Subdivision The Time Signature A system of noteheads, stems, flags and beams, has been standard- ized to notate rhythm. These symbols are used to indicate relative duration of tones. Any one of these may represent the basic pulse or beat, depending upon the time signature, which is discussed below. The notehead most commonly associated with the beat in simple-division measures is called a quarter note: "H" to hear above tune. Observe, by listening, that the quarter note does indeed represent each basic pulse (at the given tempo). There is also a regularly occuring accent every 2 quarter notes, and thus a measure (or bar) line is drawn to distinguish one grouping from another. The true meaning of the measure line is to indicate where a point of natural stress occurs. The numbers at the beginning of the tune comprise the time signature. In simple division measures, the upper number indicates the number of beats per measure, while the lower number represents the kind of note designated as the symbol for the beat, in this case a quarter note. (Please note that the time signature is not a fraction; there is no divider line which would indicate that the upper number is to be divided by the lower number, although the lower number does represent a fractional durational value). EXERCISE 3 H=Hear (to hear example) P=Prior (prior example) N=Next (next example R=Ready (to input information) + = Next page, as usual - = Previous page, as usual Use above keystrokes to hear examples (5) and answer questions. Note that some of the tunes do not begin on the first beat of a measure, but with a pickup beat (anacrusis, or upbeat); the pickup is unstressed and has the effect of leading into a stressed beat, as in the sentence "Oh I've been workin' on the Rail Road..." pickup "down" beat - 1st of measure The quarter note is normally divided into two equal sub-pulses: The note with the single flag is an eighth-note. The quarter note thus has a simple division, and so the above tunes are either duple simple, triple simple, etc., depending on how many quarter notes (beats) there are in the measure. The further sub-division of the quarter note is indicated below. (Note: the beam joins two or more flagged notes together into a unit; as a general rule, it is a good idea to beam all possible single-beat units, so that they are perceived as a unit; sometimes 4 eighth-notes are beamed together as a 2-beat unit, and sometimes 8 sixteenth-notes). Most tunes, including ones above, do not have articulations on every beat. There are inevitably times when one wishes to sustain a tone for longer than a quarter note (or a single beat). The quar- ter note bears the same relations to longer-duration notes that division of the quarter note bears to it. Two quarter notes equal a half-note; two half-notes equal a whole-note, etc., as shown below. You've probably noticed by now that in several of the tunes cited as examples, not all of the notes bear the standard durational relationship of 1:2 (quarter to eighth, eighth to sixteenth, etc), but rather have a 1:1.5 ratio, and that these notes have dots after them. The dot following a notehead lengthens the duration of the note being dotted by half again as much. Put more simply, a dot lengthens a note by half the length of the note being dotted. A new symbol, the tie, is employed in the following examples. It joins notes together as single durations. RESTS For every notehead value that may exist, there is a corresponding rest value (no sound). These are exhibited below. Dots are added to rests in the same way as they are to noteheads, to lengthen the duration of the rest by half the time of the rest dotted. Writing and Reading Rhythms Whatever the durational values of notes or rests may be, they must add up to the number of beats designated by the time signature. Among the very first things that needs to be dealt with when deploying rhythm is thus to make sure there are the proper number of durations in each measure. A second "rule of thumb" regarding rhythmic notation is to try, in the notation, to show where each beat is. In 4-beat measures, another level of organization may be perceived: 2-beat units. These issues will become clearer as we proceed. As with any aspect of music, intellectual comprehension of funda- mentals is not the same as performance, "doing" the music, either composing or performing. Performance necessitates a body/mind co- ordination that demands practice. While some people may have an inate sense of rhythm, anyone, with practice, can improve her or his rhythmic skills. Also, the reciprocal processes of writing and reading rhythms within the traditional system demands experience. The main issue in both the notating and reading of rhythms is to determine where the beat is, and to feel this beat in an internal- ized physical and consistent way. The biggest problem I have seen in working with students as composers is that few have approached understanding rhythm in a disciplined enough way to achieve a sense of feeling accurately the rhythms they are imagining. So when it comes to writing their pieces, rhythmic notation is often sloppy. This applies also to beginning music students who perhaps respond instinctively to rhythm, but who have not had to think much about what they are actually responding to. Because of this, I generally recommend the use of a metronome when learning and practicing rhythms, to assure consistency. Flexibility, that marv- elous ability to bend and shape music spontaneously and individu- ally, can come after one has acquired skill in maintaining rhythms precisely. The first premise in writing and reading rhythms is: feel the beat consistently. Then: sense the beat groupings, the number of beats that may comprise a measure. Next: sense the divisions and subdi- visions of the beat. And always remember: keep everything regular (a consistent, periodic beat). It is much better to start very slowly, maintaining accuracy and relative proportion of note values, than to attempt to do something too quickly and thereby continually alter the duration of the given beat. In notating rhythms, to state it from a slightly different angle, the prinicple is: make absolutely clear where each beat is. This is done by grouping rhythms by beats, and with a few exceptions, this means in such a way that each single beat and its division and subdivision units are readily seen. COMPOUND DIVISION Listen to the following examples (5), with particular attention directed to the number of beats per measure and the beat division. You will observe above standard 2 and 4-beat measures with more or less obvious tripartate beat division. These tunes are thus in com- pound meters. Because the notehead value designated as the beat needs to be divided into 3, compound meters use dotted values for the beat. And because a dotted note is the beat, the time signature itself cannot state directly the true number of beats in the measure. The most common notehead value for a beat in compound time is the dotted quarter. A two-beat measure would contain two of these units; a four-beat measure four of them, and so on. But convention doesn't allow us to notate this thusly: While this might be logical, the given system rather calls for us to notate compound division meters as if they have three times as many beats, with the upper number thus representing the number of divisions in a measure and the lower number indicating the kind of durational value which represents the division rather than the beat. A two-beat compound-division meter, using the dotted quarter as the beat, is thus, as represented in the common folk tune "The Irish Washerwoman:" Because the tempo is sufficiently fast here, rather than hearing each eighth-note as a beat, we hear the eighth-notes grouped into threes. All compound division meters have an upper number divisible by 3 (except 3 itself, which is usually grouped with the simple-division meters). Dividing the upper number by 3 reveals the number of beats in the measure, while adding 3 of the lower number values together reveals the notehead value of the beat. The relationship of the dotted quarter to its division and subdi- vision is as follows: Note that the subdivision of a compound beat traditionally divides the division into 2, not 3. The relation of the dotted quarter to larger duration notes in compound meters is: EXERCISE H=Hear N=Next P=Prior R=Ready A=Answer +,- per usual H.= dotted half Q.= dotted quarter Q= quarter E.= dotted eighth E= eighth S = sixteenth Listen to example. When ready, hit "R" and enter durational values. (4-beat pattern is preceded by 4 beats to establish tempo). BORROWED DIVISION If rhythmic structures contain sub-pulses that are half the length of the beat, the meter is simple; if the sub-pulses are a third the length of the beat, the meter is compound. For variety, in simple-division meters one may occasionally employ a compound division unit, and vice-versa. This is technically considered to be a "borrowing" of the common division from the "opposite" config- uration, simple/compound. Such borrowings must be specially marked. When in a simple-division meter, the compound "borrowing" is called a triplet. The comparable unit in a compound-division meter is a duplet.